1. THE DEADLINE-BASED SCHEDULING OF DIVISIBLE REAL-TIME WORKLOADS ON MULTIPROCESSOR PLATFORMS Suriayati Chuprat Supervisors: Professor Dr Shaharuddin Salleh Professor Dr Sanjoy K. Baruah INSPIRING CREATIVE AND INNOVATIVE MINDS

2. Presentation Contents Introduction Summary of Contributions Anomalous Observations & Theoretical Explanations Optimal Algorithm --MINPROCS LP-Based Algorithm --MIN-ξ Conclusions INSPIRING CREATIVE AND INNOVATIVE MINDS

3. Introduction Formal models for representing real-time workloads –Uniprocessor environments –One particular restriction: each task may execute upon at most one processor at each instant in time. –Liu pointed out [8], “the simple fact that a [job] can use only one processor even when several processors are free at the same time adds a surprising amount of difficulty to the scheduling of multiple processors"

4. Divisible workload, –Arrival time, A i ≥ 0 –Total data size of a job,  i >0 –Relative deadline, D i >0, A i +D i DLT allows for the simultaneous execution of a job upon multiple processors Real-time DLT

5. DLT Computing Cluster = (N, C p, C m ) N – Number of processing nodes C p – Time taken to process C m – Time taken to transmit P0P0 P1P1 P2P2 P3P3 PNPN … Real-time DLT

6. nCpnCp 2Cm2Cm 3Cm3Cm 1Cm1Cm nCmnCm P0P0 1Cp1Cp 2Cp2Cp 3Cp3Cp P1P1 P2P2 P3P3 PnPn Data transmission and execution time diagram  =C p /(C p +C m ) r1r1 r2r2 r3r3 rnrn nCpnCp 2Cm2Cm 3Cm3Cm 1Cm1Cm nCmnCm 1Cp1Cp 2Cp2Cp 3Cp3Cp when processors have different ready times Real-time DLT

7. “Given a divisible load of size  and processor ready-times r 1, r 2,…, what is the minimum number of processors needed to meet a job’s deadline?” Approach by Lin et al. in [9] –Abstraction of heterogeneous clusters –Approximation Non-optimal Computing Min-N

8. When allocating processors in order to meet a divisible job's deadline, a scheduling algorithm must know the minimum number required by the job When all the processors are allocated simultaneously, recall that the completion time is given by: The minimum number of processors needed is computed from this equation by setting this completion time to the job's deadline (A + D) Computing Min-N

9. When the processors have different ready times, using the previous approach is more challenging Lin et al. (9,7) –Map processors to heterogeneous clusters of virtual processors with different speeds (C pi ) –Derive a formula to determine C pi as –Approximation ** there is a circularity of reasoning going on here Computing Min-N

10. Algorithm--MINPROCS

11. –x–x Simulation Results

12. –x–x

13. “Given a divisible load of size  and n (identical) processors with ready-times r 1,…, r n upon which to execute it, what is the earliest time at which  can complete execution?” Approach by Lin et al. in [9] –Abstraction to heterogeneous clusters –Compute the fractions of load to be assigned to each virtual processor –Compute the completion time Non-optimal Computing Completion Time

14. Computing the completion time: LP formulation  i : fraction of load assigned to P i r i : ready time of P i s i : time data transmission begin to P i  : Completion time  i : fraction of load assigned to P i r i : ready time of P i s i : time data transmission begin to P i  : Completion time Computing Completion Time

16. RT-DLT has the potential to provide a solid theoretical foundation to real-time distributed clusters We have studied two scheduling problems in RT-DLT when applied to clusters with different available times: –How does one compute the minimum number of processors needed to meet a job's deadline? –Given a number of processors, how does one determine the earliest completion time for the job on this many processors? For both problems, we provide exact solutions Conclusion